Effective size and the persistence of ecosystems

Ecosystems distributed in space have an effective size, reflecting both their absolute size (extent) and their fine-scale physical structure (viscosity). In this paper, a general mathematical model of a predator-prey interaction is presented via the phase-plane graphs of Rosenzweig and MacArthur (1963) to show one reason why ecosystems of larger effective size should persist longer than smaller ones: oscillations of population densities tend to be displaced farther from extinction thresholds-even in spatially homogeneous systems. Experimental results obtained by Gause and Luckinbill with protozoa and Huffaker with mites are interpreted in this context.